It was the fifth official depreciation this week, prompted by the widening gap between the black market and the official rate.
The bank offered $40 million and sold $38.4 million at a cutoff price of 7.3901 pounds per dollar, the central bank said.
The rates at which banks are allowed to trade dollars are determined by the results of central bank sales, giving the bank effective control over official exchange rates.
But there remains an active black market in the pound that is used by businesses and individuals, and the gap between this and the official rate had been widening for months.
The pound was trading at 7.89 to the dollar on the black market shortly after the central bank's auction on Thursday, according to one trader. Another trader put the rate at 7.87.
That was slightly stronger than the black market rate on Wednesday, when several traders put the average rate at 7.93. Earlier in the week, traders said the rate rose to eight pounds per dollar on no demand for dollars in the unofficial market.
Expectations that the bank would devalue had grown since it announced a surprise 50-basis-point cut in benchmark interest rates on Thursday last week, saying that plummeting global oil prices had eased the inflation outlook.